[OSM-dev] Nearest way for a location

["Marc Schütz"]

> Example:
> 
>   Your coordinates (G): (2, 3)
>   Your road segment (AB): (1, 1) -> (4, 5)
> 
>   Therefore you get:
>   Function for all points on AB: (1, 1) + t*(3, 4)   (for 0<=t<=1)
>   Normal vector to AB (n): (-4, 3)
>   Unified normal vector to AB (n0): (-4/5, 3/5) = (-0.8, 0.6)
> 
> 
> You can use the hesse normal form to calculate the distance (which is the
> easier solution):
> 
>   Hesse normal form: n0 * (X - A)       (for X is any point on AB)
>   Our Hesse normal form of that line: (-0.8, 0.6) * (X - (1, 1)) = 0
> 
>   Distance form: | AG * n0 |     ( * being a scalar product )
>   Our distance: | (1, 2) * (-0.8, 0.6) | = | -0.8 + 1.2 |
> 
> -> distance: 0.4

The length of a vector (a,b) is sqrt(a^2 + b^2), not abs(a+b)!
Thus |(1,2) * (-0.8,0.6)| = |-0.8,1.2| = sqrt(0.64+1.44) = sqrt(2.08) ~ 1.44

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